You can play Full Screen mode and alt+tab to use it's internet browser if you add FFXIV to Steam and play through that. I still use Windowed mode and Shift Window as I prefer to use my own Browser but performance does take a hit.
Also wish the Com Reps would stop passing this off as a suggestion when clearly it isn't. It is a bug and fault in the game. Hell if you play Full Screen mode and accidentally hit the Windows key the game crashes, how can that not be a bug. Really beggars belief that SE have not announced any plans to tackle this issue.
Technically he is correct it could be seen as a violation of the TOS but I really would be surprised if SE banned anyone over this because they lack the ability to code basic features into a game.